Chapter 13

The term "proof," still used to describe the ethanol content of alcoholic beverages, originated in seventeenthcentury England. A sample of whiskey was poured on gunpowder and set afire. If the gunpowder ignited after the whiskey had burned off, this "proved" that the whiskey had not been watered down. The minimum ethanol content for a positive test was about \(50 \%\) by volume. The \(50 \%\) ethanol solution became known as \(^{\prime \prime} 100\) proof." Thus, an 80 -proof whiskey would be \(40 \% \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) by volume. Listed in the table below are some data for several aqueous solutions of ethanol. With a minimum amount ofcalculation, determine which of the solutions are more than 100 proof. Assume that the density of pure ethanol is \(0.79 \mathrm{g} / \mathrm{mL}\).$$\begin{array}{cl} \hline \text { Molarity of Ethanol, } M & \text { Density of Solution, g/mL } \\\ \hline 4.00 & 0.970 \\\5.00 & 0.963 \\\6.00 & 0.955 \\\7.00 & 0.947 \\\8.00 & 0.936 \\\9.00 & 0.926 \\\10.00 & 0.913 \\\\\hline\end{array}.$$

Hydrogen chloride is a colorless gas, yet when a bottle of concentrated hydrochloric acid \([\mathrm{HCl}(\mathrm{conc} \text { aq) }]\) is opened, mist-like fumes are often seen to escape from the bottle. How do you account for this?

Nitrobenzene, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NO}_{2},\) and benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) are completely miscible in each other. Other properties of the two liquids are nitrobenzene: \(\mathrm{fp}=5.7^{\circ} \mathrm{C}, K_{\mathrm{f}}=\) \(8.1^{\circ} \mathrm{C} m^{-1} ;\) benzene: \(\mathrm{fp}=5.5^{\circ} \mathrm{C}, K_{\mathrm{f}}=5.12^{\circ} \mathrm{C} m^{-1} . \mathrm{It}\) is possible to prepare two different solutions with these two liquids having a freezing point of \(0.0^{\circ} \mathrm{C}\) What are the compositions of these two solutions, expressed as mass percent nitrobenzene?

Suppose that \(1.00 \mathrm{mg}\) of gold is obtained in a colloidal dispersion in which the gold particles are spherical, with a radius of \(1.00 \times 10^{2} \mathrm{nm}\). (The density of gold is \(\left.19.3 \mathrm{g} / \mathrm{cm}^{3} .\right)\) (a) What is the total surface area of the particles? (b) What is the surface area of a single cube of gold of mass \(1.00 \mathrm{mg} ?\)

Instructions on a container of antifreeze (ethylene glycol; \(\left.\mathrm{fp},-12.6^{\circ} \mathrm{C}, \mathrm{bp}, 197.3^{\circ} \mathrm{C}\right)\) give the following volumes of Prestone to be used in protecting a \(12 \mathrm{qt}\) cooling system against freeze-up at different temperatures (the remaining liquid is water): \(10^{\circ} \mathrm{F}, 3 \mathrm{qt}\) \(0^{\circ} \mathrm{F}, 4 \mathrm{qt} ;-15^{\circ} \mathrm{F}, 5 \mathrm{qt} ;-34^{\circ} \mathrm{F}, 6 \mathrm{qt} .\) since the freezing point of the coolant is successively lowered by using more antifreeze, why not use even more than 6 qt of antifreeze (and proportionately less water) to ensure the maximum protection against freezing?

At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{O}_{2}(\mathrm{g})\) in water is \(28.31 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{N}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{N}_{2}(\mathrm{g})\) in water is \(14.34 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) The composition of the atmosphere is \(78.08 \% \mathrm{N}_{2}\) and \(20.95 \% \mathrm{O}_{2},\) by volume. What is the composition of air dissolved in water expressed as volume percents of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ?\)

A saturated solution prepared at \(70^{\circ} \mathrm{C}\) contains \(32.0 \mathrm{g}\) CuSO \(_{4}\) per 100.0 g solution. A 335 g sample of this solution is then cooled to \(0^{\circ} \mathrm{C}\) and \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) crystallizes out. If the concentration of a saturated solution at \(0^{\circ} \mathrm{C}\) is \(12.5 \mathrm{g} \mathrm{CuSO}_{4} / 100 \mathrm{g}\) soln, what mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) would be obtained? [Hint: Note that the solution composition is stated in terms of \(\mathrm{CuSO}_{4}\) and that the solid that crystallizes is the hydrate \(\left.\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} .\right]\)

The concentration of Ar in the ocean at \(25^{\circ} \mathrm{C}\) is \(11.5 \mu \mathrm{M} .\) The Henry's law constant for \(\mathrm{Ar}\) is \(1.5 \times 10^{-3}\) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{atm}^{-1} .\) Calculate the mass of \(\mathrm{Ar}\) in a liter of ocean water. Calculate the partial pressure of \(\mathrm{Ar}\) in the atmosphere.

The concentration of \(\mathrm{N}_{2}\) in the ocean at \(25^{\circ} \mathrm{C}\) is \(445 \mu \mathrm{M} .\) The Henry's law constant for \(\mathrm{N}_{2}\) is \(0.61 \times 10^{-3} \mathrm{mol} \mathrm{L}^{-1} \mathrm{atm}^{-1} .\) Calculate the mass of \(\mathrm{N}_{2}\) in a liter of ocean water. Calculate the partial pressure of \(\mathrm{N}_{2}\) in the atmosphere.

A solution contains \(750 \mathrm{g}\) of ethanol and \(85.0 \mathrm{g}\) of sucrose \(\left(180 \mathrm{g} \mathrm{mol}^{-1}\right) .\) The volume of the solution is \(810.0 \mathrm{mL} .\) Determine (a) the density of the solution (b) the percent of sucrose in the solution (c) the mole fraction of sucrose (d) the molality of the solution (e) the molarity of the solution

What volume of ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH},\right.\) density \(=1.12 \mathrm{g} \mathrm{mL}^{-1}\) ) must be added to \(20.0 \mathrm{L}\) of water \(\left(K_{\mathrm{f}}=1.86^{\circ} \mathrm{C} / m\right)\) to produce a solution that freezes at \(-10^{\circ} \mathrm{C} ?\)

Every year, oral rehydration therapy (ORT)-the feeding of an electrolyte solution-saves the lives of countless children worldwide who become severely dehydrated as a result of diarrhea. One requirement of the solution used is that it be isotonic with human blood.(a) One definition of an isotonic solution given in the text is that it have the same osmotic pressure as \(0.92 \% \mathrm{NaCl}(\mathrm{aq})\) (mass/volume). Another definition is that the solution have a freezing point of \(-0.52^{\circ} \mathrm{C}\) Show that these two definitions are in reasonably close agreement given that we are using solution concentrations rather than activities.(b) Use the freezing-point definition from part (a) to show that an ORT solution containing \(3.5 \mathrm{g} \mathrm{NaCl}\) \(1.5 \mathrm{g} \mathrm{KCl}, 2.9 \mathrm{g} \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\) (sodium citrate), and \(20.0 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose) per liter meets the requirement of being isotonic. [Hint: Which of the solutes are nonelectrolytes, and which are strong electrolytes?]

Briefly describe each of the following ideas or phenomena: (a) Henry's law; (b) freezing-point depression; (c) recrystallization; (d) hydrated ion; (e) deliquescence.

Explain the important distinctions between each pair of terms: (a) molality and molarity; (b) ideal and nonideal solution; (c) unsaturated and supersaturated solution; (d) fractional crystallization and fractional distillation; (e) osmosis and reverse osmosis.

The most likely of the following mixtures to be an ideal solution is (a) \(\mathrm{NaCl}-\mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}-\mathrm{C}_{6} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{H}_{2} \mathrm{O} ;\) (d) \(\mathrm{C}_{7} \mathrm{H}_{16}-\mathrm{C}_{8} \mathrm{H}_{18}\)

The solubility of a nonreactive gas in water increases with (a) an increase in gas pressure; (b) an increase in temperature; (c) increases in both temperature and pressure; (d) an increase in the volume of gas in equilibrium with the available water.

Of the following aqueous solutions, the one with the lowest freezing point is (a) \(0.010 \mathrm{mgSO}_{4} ;\) (b) \(0.011 \mathrm{m}\) \(\mathrm{NaCl} ;(\mathrm{c}) 0.018 \mathrm{m} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} ;(\mathrm{d}) 0.0080 \mathrm{m} \mathrm{MgCl}_{2}\).

An ideal liquid solution has two volatile components. In the vapor in equilibrium with the solution, the mole fractions of the components are (a) both \(0.50 ;\) (b) equal, but not necessarily \(0.50 ;\) (c) not very likely to be equal; (d) 1.00 for the solvent and 0.00 for the solute.

NaCl(aq) isotonic with blood is \(0.92 \%\) NaCl (mass/volume). For this solution, what is (a) \(\left[\mathrm{Na}^{+}\right]\) (b) the total molarity of ions; (c) the osmotic pressure at \(37^{\circ} \mathrm{C} ;\) (d) the approximate freezing point? (Assume that the solution has a density of 1.005 g/mL.)

Which aqueous solution from the column on the right has the property listed on the left? Explain your choices. $$\begin{array}{ll}\hline \text { Property } & \text { Solution } \\\\\hline \text { 1. lowest electrical } & \text { a. } 0.10 \mathrm{m} \mathrm{KCl}(\mathrm{aq}) \\\\\text { conductivity } & \\\\\text { 2. } \text { lowest boiling } & \text { b. } 0.15 \mathrm{m}\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(\mathrm{aq}) \\\\\text { point } & \\\\\text { 3. highest vapor pressure } & \text { c. } 0.10 \mathrm{m} \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}) \\\\\text { of water at } 25^{\circ} \mathrm{C} & \\\\\text { 4. lowest freezing point } & \text { d. } 0.05 \mathrm{m} \mathrm{NaCl} \\\\\hline\end{array}$$

Which of the following ions has the greater charge density? (a) \(\mathrm{Na}^{+} ;\) (b) \(\mathrm{F}^{-} ;\) (c) \(\mathrm{K}^{+} ;\) (d) \(\mathrm{Cl}^{-}\).

When \(\mathrm{NH}_{4} \mathrm{Cl}\) dissolves in a test tube of water, the test tube becomes colder. Is the magnitude of \(\Delta \mathrm{H}_{\text {lattice }}\) for \(\mathrm{NH}_{4} \mathrm{Cl}\) larger or smaller than the sum of \(\Delta \mathrm{H}_{\text {hydration }}\) of the ions?

In a saturated solution at \(25^{\circ} \mathrm{C}\) and 1 bar, for the following solutes, which condition will increase solubility? (a) \(\operatorname{Ar}(g),\) decrease temperature; (b) \(\mathrm{NaCl}(\mathrm{s})\) increase pressure; (c) \(\mathrm{N}_{2}\), decrease pressure; (d) \(\mathrm{CO}_{2}\) increase volume.

What is the weight percent of \(23.4 \mathrm{g}\) of \(\mathrm{CaF}_{2}\) if dissolved in 10.5 mol of water? (a) \(0.028\); (b)\( 1.59\);(c) \(11.0\); (d) \(12.4 ;\) (e) none of these.